joint work with Christian Kanzow, Daniel Steck
Mathematical programs with switching constraints are characterized by restrictions requiring the product of two functions to be zero. Switching structures appear frequently in the context of optimal control and can be used to reformulate semi-continuity conditions on variables or logical or-constraints. In this talk, these applications of switching-constrained optimization are highlighted. Moreover, first-and second-order optimality conditions for this problem class will be investigated. Finally, a relaxation method is suggested and results of computational experiments are presented.
In this talk, we present a directional version of pseudo-normality for very general constraints. This condition implies the prominent error bound property/MSCQ. Moreover, it is naturally milder than its standard (non-directional) counterpart, in particular GMFCQ, as well as the directional FOSCMS. We apply the obtained results to the disjunctive programs, where pseudo-normality assumes a simplified form, resulting in verifiable point-based sufficient conditions for this property and hence also for MSCQ. In particular, we recover SOSCMS and the Robinson's result on polyhedral multifunctions.
joint work with Matúš Benko, Tim Hoheisel
We introduce a class of ortho-disjunctive programs (ODPs), which includes MPCCs, MPVCs and several further recently introduced examples of disjunctive programs. We present a tailored directional version of quasi-normality introduced for general constraint systems which implies error bound property/metric subregularity CQ. Thus, we effectively recover or improve some previously established results. Additionally, we introduce tailored OD-versions of stationarity concepts and strong CQs (LICQ, MFCQ etc) and provide a unifying framework for further results on stationarity conditions for all ODPs.